$$$\frac{\csc^{2}{\left(x \right)}}{9}$$$의 적분

$$$\int \frac{\csc^{2}{\left(x \right)}}{9}\, dx$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$을 $$$c=\frac{1}{9}$$$와 $$$f{\left(x \right)} = \csc^{2}{\left(x \right)}$$$에 적용하세요:

$${\color{red}{\int{\frac{\csc^{2}{\left(x \right)}}{9} d x}}} = {\color{red}{\left(\frac{\int{\csc^{2}{\left(x \right)} d x}}{9}\right)}}$$

$$$\csc^{2}{\left(x \right)}$$$의 적분은 $$$\int{\csc^{2}{\left(x \right)} d x} = - \cot{\left(x \right)}$$$:

$$\frac{{\color{red}{\int{\csc^{2}{\left(x \right)} d x}}}}{9} = \frac{{\color{red}{\left(- \cot{\left(x \right)}\right)}}}{9}$$

따라서,

$$\int{\frac{\csc^{2}{\left(x \right)}}{9} d x} = - \frac{\cot{\left(x \right)}}{9}$$

적분 상수를 추가하세요:

$$\int{\frac{\csc^{2}{\left(x \right)}}{9} d x} = - \frac{\cot{\left(x \right)}}{9}+C$$

$$$\int \frac{\csc^{2}{\left(x \right)}}{9}\, dx = - \frac{\cot{\left(x \right)}}{9} + C$$$A